1. Use a transistor to switch the display's +5v on/off using a digital pin. Then you would need to initialize the display every time to switch it on.

2. Use one or two digital pins to control the backlight and contrast of the LCD. If you feed the positive side of the contrast pot with a digital pin, you can easily "switch off" the display with a single digitalWrite(). Remember to control the backlight in the same way.

I prefer (2). It's a lot less hassle as you only need to initalise the LCD once.